Electroerosion is mentioned as an example of a non-contact removal process. This is based on a material removal between electrically conductive contacts. An electrically conductive contact is formed by a workpiece. A further contact is formed by a shaping tool, for example by a wire. The tool is brought close to the workpiece without coming into contact therewith. By applying an electrical voltage between the tool and the workpiece, an arc or a spark is produced for a short period of time, by means of which material can be detached from the workpiece and removed. If the tool is a thin wire which is fed towards the workpiece in the axial direction, bores can then be introduced in the workpiece, for example bores having a diameter of less than 1 millimeter, for example 0.2 millimeter. Such bores are, for example, restrictor bores in injection valves of internal combustion engines. The formation of such bores can be very time-consuming.